With all of the restrictions, how can we effectively witness in the workplace?

Many of the restrictions implied in your question are enforced illegally. It is vital that you know the law so that you can stand firm in your faith, knowing that you are legally protected.

The First Amendment is your friend! Its guarantee of free speech means that employees can talk about their personal beliefs to the same degree that other employees might talk about their favorite football teams. For example, an employer may not legally allow joke e-mails to be distributed but then restrict religious e-mails. They cannot allow family pictures to be hung on office walls but deny the right to hang a framed picture of Jesus Christ. They cannot allow one employee to hold a weight loss clinic in the
conference room during the lunch hour, but then forbid another employee to have a Bible study in that same conference room before work hours.

The key is that witnessing and other religious discussions or meetings cannot be mandatory and they cannot interfere with work efficiency or productivity. Outside of those parameters, you are free to discuss your beliefs and to witness to others.